A new generation of council houses should be built to overcome a "big shortage", the shadow housing minister, Emma Reynolds, has said.

Reynolds, who will accuse the government in a speech on Monday of presiding over the lowest levels of housebuilding since the 1920s, said that the government has failed to bring forward an investment programme in social housing.

Speaking on the Sunday Politics on BBC1, Reynolds said: "We've called on this government to bring forward investment in social housing. We want to see an investment programme in social housing … I want to see a council house-building programme because there is a very big shortage of council homes."

It is understood Reynolds was not committing Labour to an expensive new programme of council house-building, but was instead highlighting the issue's importance and saying that a new programme should be a priority if the public finances permit.

In her speech, Reynolds will say that the housing market has a "broken gearstick", creating a housing shortage which is central to the cost of living crisis highlighted by Ed Miliband. She will tell the National House Building Council: "As currently structured, our country's building sector has a broken gearstick. When the time comes to shift up a gear, our housebuilding industry is found wanting."

Reynolds will say that a future Labour government would require local authorities to include a higher proportion of small sites open for development by including them in their five year land supply.

There would also be guaranteed access to public land to smaller house builders and so called "custom builders" who allow people to build their own homes. They would be guaranteed the right to build a proportion of homes in a new generation of new towns and garden cities.

She will say: "We know that one of the key barriers for small and custom builders is access to land. That's why I am announcing today 'Build First' – a package of measures to assemble an army of smaller firms and custom builders to tackle the housing shortage and help the next generation on to the property ladder.

"The next Labour government will require local authorities to include a higher proportion of small sites in their five-year land supply. Second, we will give guaranteed access to public land to smaller firms and custom builders. And we will ensure that any public land given over for housebuilding will have a proportion dedicated for this purpose."